CAIRO, Sept 22 (Reuters) - Several Egyptian students were arrested on Sunday as the start of a new academic year was marked by protests against the army-backed government and clashes between supporters and opponents of deposed Islamist President Mohamed Mursi.

A Cairo court is due to rule on Monday on whether Mursi's Muslim Brotherhood should be dissolved, a verdict which could trigger more protests and violence. Nearly 1,000 people were killed after the army ousted Mursi in July after mass protests.

Mursi supporters staged small protests in universities in cities including Cairo and Alexandria, and students were arrested across the country, media and security sources said. There was no figure available for the number of arrests.

Eleven students were injured in clashes in Mursi's home town, Zakazik, according to the website of the Al-Masry Al-Youm daily.

"Down, down with the rule of the coup," dozens of pro-Mursi students at Cairo University chanted, witnesses said.

Seventeen-year-old student Sarah Adel Ibrahim was handed to authorities by residents of El-Menoufia, a town in the Nile Delta, after she wrote "down with military rule" on the walls of a school, the state-run Al-Ahram news website said.

Two high school students were arrested in the city of Marsa Matrouh for distributing flyers calling on students to boycott school in protest at the "coup", a security source said.

"The two students were caught distributing flyers accusing the army and police of being killers," the source said.

Over 2,000 Islamist activists, mostly from Mursi's Muslim Brotherhood, have been arrested in the past two months. (Reporting and writing by Yasmine Saleh, additional reporting by Omar Fahmy; Editing by Robin Pomeroy)